Safe Haskell	Safe-Inferred
Language	Haskell2010

Deka.Native

Contents

Digits and groups of digits
Elements of abstract numbers
Transformations

Description

Representation of numbers in native Haskell types.

Since deka is a binding to the mpdecimal C library, the data types are held as pointers to data which are managed by C functions. Therefore there is no direct access to what is inside of the the Dec data type. Modules in Deka.Native provide Haskell types mirroring the abstract representations given in the General Decimal Arithmetic Specification. This is useful if you want to manipulate the data in an abstract way. For example, perhaps you want to perform arithmetic on a value, transform it to abstract form, add digit grouping characters, and then use your own functions to pretty print the result.

The General Decimal Arithmetic Specification gives an abstract representation of each number. This information is taken from the General Decimal Arithmetic specification at

http://speleotrove.com/decimal/damodel.html

A number may be finite, in which case it has three components: a sign, which must be zero (for zero or positive numbers) or one (for negative zero and negative numbers), an integral coefficient, which is always zero or positive, and a signed integral exponent, which indicates the power of ten by which the number is multiplied. The value of a finite number if given by

(-1) ^ sign * coefficient * 10 ^ exponent

In addition to finite numbers, a number may also be one of three special values:

infinity - numbers infinitely large in magnitude
quiet NaN - an undefined result which does not cause an invalidOperation condition.
signaling NaN - an undefined result which will usually cause an invalidOperation condition.

When a number has one of these special values, its coefficient and exponent are undefined. An NaN, however, may have additional diagnostic information, which is a positive integer.

All special values have a sign. The sign of an infinity is significant. The sign of an NaN has no meaning, though it may be considered as part of the diagnostic information.

You can transform an abstract form to a Dec losslessly by using abstractToByteString. This gives you a string in scientific notation, as specified in to-scientific-string in the specification. There is a one-to-one mapping of abstract representations to scientific-string representations. You can also transform a Dec to an Abstract losslessly by using abstractFromByteString. This operation will not fail if it is using output from toByteString; but it might fail otherwise, if the input is malformed.

All standard typeclass instances in these modules are derived; so while the Ord instance might be useful to use Abstract as the key in a Map, don't expect it to tell you anything about how Abstract are situated on the number line.

Synopsis

Digits and groups of digits

data Novem Source

A digit from one to nine. Useful to represent a most significant digit, or MSD, as an MSD cannot be the digit zero.

Constructors

D1
D2
D3
D4
D5
D6
D7
D8
D9

Instances

Bounded Novem
Enum Novem
Eq Novem
Ord Novem
Show Novem

data Decem Source

A digit from zero to nine.

Constructors

D0
Nonem Novem

Instances

Eq Decem
Ord Decem
Show Decem

data Decuple Source

A non-empty set of digits. The MSD must be from 1 to 9.

Constructors

Decuple Novem [Decem]

Instances

Eq Decuple
Ord Decuple
Show Decuple

data Aut Source

Either a set of digits, or zero. Unsigned.

Constructors

Nil	Zero
Plenus Decuple	Non-zero

Instances

Eq Aut
Ord Aut
Show Aut

data Firmado Source

Either a set of digits, or zero. Signed.

Constructors

Cero	Zero
Completo PosNeg Decuple	Non-zero

Instances

Eq Firmado
Ord Firmado
Show Firmado

Elements of abstract numbers

newtype Coefficient Source

The coefficient in a number; not used in infinities or NaNs.

Constructors

Coefficient
Fields unCoefficient :: Aut

Instances

Eq Coefficient
Ord Coefficient
Show Coefficient

newtype Exponent Source

The exponent in a number.

Constructors

Exponent
Fields unExponent :: Firmado

Instances

Eq Exponent
Ord Exponent
Show Exponent

newtype Diagnostic Source

The diagnostic information in an NaN.

Constructors

Diagnostic
Fields unDiagnostic :: Decuple

Instances

Eq Diagnostic
Ord Diagnostic
Show Diagnostic

data Noisy Source

Whether an NaN is quiet or signaling.

Constructors

Quiet
Signaling

Instances

Eq Noisy
Ord Noisy
Show Noisy

data NonNum Source

Not a Number.

Constructors

NonNum
Fields noisy :: Noisy diagnostic :: Maybe Diagnostic

Instances

Eq NonNum
Ord NonNum
Show NonNum

data Value Source

All data in an abstract number except for the sign.

Constructors

Finite Coefficient Exponent
Infinite
NotANumber NonNum

Instances

Eq Value
Ord Value
Show Value

data Abstract Source

Abstract representation of all numbers covered by the General Decimal Arithmetic Specification.

Constructors

Abstract
Fields sign :: Sign value :: Value

Instances

Eq Abstract
Ord Abstract
Show Abstract

Transformations

abstractToString :: Abstract -> String Source

Transform an Abstract to a String. This conforms to the to-scientific-string transformation given in the General Decimal Arithmetic Specification at

http://speleotrove.com/decimal/daconvs.html#reftostr

with one exception: the specification provides that some finite numbers are represented without exponential notation. abstractToString always uses exponential notation on finite numbers.

abstractToDec :: Abstract -> (Dec, Flags) Source

Transforms an Abstract to a Dec. Result is computed in a context using the Pedantic initializer. Result is returned along with any status flags arising from the computation.

stringToAbstract Source

Arguments

:: String	Input string
-> Either String Abstract	Returns a Right with the abstract representation of the input string, if the input conformed to the numeric string specification given in the General Decimal Arithmetic Specification. Otherwise, returns a Left with an error message.

decToAbstract :: Dec -> Abstract Source

Transforms a Dec to an Abstract.